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- W2023172986 abstract "Abstract We construct a continuous distribution G such that the number of faces in the smallest concave majorant of the random walk with G -distributed summands will take on each natural number infinitely often with probability one. This investigation is motivated by the fact that the number of faces F n of the concave majorant of the random walk at time n has the same distribution as the number of records R n in the sequence of summands up to time n . Since R n is almost surely asymptotic to log n , the construction shows that despite the equality of all of the one-dimensional marginals, the almost sure behaviors of the sequences { R n } and { F n } may be radically different." @default.
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- W2023172986 date "2005-11-01" @default.
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- W2023172986 title "Random walks whose concave majorants often have few faces" @default.
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- W2023172986 doi "https://doi.org/10.1016/j.spl.2005.05.012" @default.
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